Tool coupling between two coupling parts, and coupling part for such a tool coupling

A tool coupling between two coupling parts extending in an axial direction, in particular between a cutting head and a carrier of a rotary tool, with a predefined direction of rotation, wherein the first coupling part—in particular the cutting head—comprises a clamping pin with a pair of clamping sections that are opposite one another on sides of the pin, and the second coupling part—in particular the carrier—comprises a pin receptacle with a pair of clamping sections that are opposite one another on sides of the receptacle, and wherein the clamping pin can be clamped by turning it counter to the direction of rotation about an axis of rotation into the pin receptacle so that clamping sections of the clamping pin and the pin receptacle that correspond to one another produce a press fit,

• wherein
• each clamping section respectively comprises several successive clamping surfaces, which—in a cross section when viewed orthogonally to the axial direction—travel respectively along a circular arc having a predefined diameter, wherein the diameter of the clamping surfaces that are successive in the direction of rotation increases.